## Welcome to BrainDen.com - Brain Teasers Forum

Welcome to BrainDen.com - Brain Teasers Forum. Like most online communities you must register to post in our community, but don't worry this is a simple free process. To be a part of BrainDen Forums you may create a new account or sign in if you already have an account. As a member you could start new topics, reply to others, subscribe to topics/forums to get automatic updates, get your own profile and make new friends. Of course, you can also enjoy our collection of amazing optical illusions and cool math games. If you like our site, you may support us by simply clicking Google "+1" or Facebook "Like" buttons at the top. If you have a website, we would appreciate a little link to BrainDen. Thanks and enjoy the Den :-) |

Guest Message by DevFuse

# Sum of n consecutive integers

Started by BMAD, Jul 13 2013 02:25 AM

4 replies to this topic

### #1

Posted 13 July 2013 - 02:25 AM

You may already know that 1+2+3+4+5=15. Let's try five other consecutive integers: 14+15+16+17+18=80. How about -1+0+1+2+3=5? We might guess that the sum of 5 consecutive integers is divisible by 5. That turns out to be true. Maybe the sum of n consecutive integers is divisible by n. That turns out not to be true: 1+2 is not divisible by 2.

Question: When is the sum of n consecutive integers divisible by n, and when is it not divisible by n?

### #2

Posted 13 July 2013 - 02:46 AM

Spoiler for

### #3

Posted 13 July 2013 - 03:15 AM

Spoiler for

this is correct but can you prove it?

### #4

Posted 13 July 2013 - 12:00 PM

Spoiler for

### #5

Posted 13 July 2013 - 05:43 PM Best Answer

Spoiler for

Spoiler for

**Edited by BMAD, 13 July 2013 - 05:43 PM.**

#### 0 user(s) are reading this topic

0 members, 0 guests, 0 anonymous users